Sedeonic Field Equations for Dyons

Миронов, В. Л.; Mironov, Sergey V.

doi:10.1007/s00006-018-0886-3

Cited by 12 publications

(9 citation statements)

References 32 publications

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“…Because of the different spatial and temporal symmetries in terms of various physical systems, the Maxwell equations with monopole term denoted in Eq. (15) are invariant under the electromagnetic duality transformations in general forms [38]:…”

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

“…where the α and β terms denote any parameters. After Coceal et al's work in [4] in terms of the electromagnetic duality form, Mironov and Mironov developed new duality notations for dyons that satisfy the transformation matrix equal to +1 [38].…”

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

“…In the case of dyons, the duality-invariant electric and magnetic fields can be defined by using Coceal's suggestion [4,6] and reforming Mironov's developments [38] in the following form:…”

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

“…It is easily seen that equations (34) and (35) are similar to each other with the above duality operations. In order to have more detailed expressions, one can use the equalities of dyonic systems in the framework of Mironov's paper [38].…”

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

“…Here, the duality-invariant fields ⃗ E and ⃗ B are not the physical fields. They are quantities, which occurred from linear combinations of ⃗ E electric field and ⃗ B magnetic induction [4,6,38]. λ is the impact constant depending on electric and magnetic charges in the form of λ = √ e 2 + g 2 .…”

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

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Octonion form of duality-invariant field equations for dyons

Kansu¹,

Tanışlı²,

Demir³

2020

Turk J Phys

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The hypothetical particles dyons, which carry both electric and magnetic charges simultaneously, are widely discussed in application to electromagnetic theory and magnetohydrodynamics. Particularly, the duality-invariant field equations were suggested with suitable definitions of the dyon's electromagnetic characteristics. In this study, we propose an alternative formulation of the duality-invariant field equations for dyons based on octonion algebra. Octonions have been used to express the equations for potentials, field strengths, and sources in a more compact and consistent manner.Additionally, the octonionic form of the energy conservation law for dyons has been derived.

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Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

“…In the case of dyons, the duality-invariant electric and magnetic fields can be defined by using Coceal's suggestion [4,6] and reforming Mironov's developments [38] in the following form:…”

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

Section: Duality-invariant Field Equations For Dyonsmentioning

confidence: 99%

See 3 more Smart Citations

Octonion form of duality-invariant field equations for dyons

Kansu¹,

Tanışlı²,

Demir³

2020

Turk J Phys

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Gauge fields and four interactions in the trigintaduonion spaces

Weng

2024

Math Methods in App Sciences

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The paper aims to apply the trigintaduonion spaces to explore the physical properties of four interactions simultaneously, including the electromagnetic fields, gravitational fields, weak nuclear fields, and strong nuclear fields. J. C. Maxwell first applied the algebra of quaternions to study the physical properties of electromagnetic fields. It inspired some subsequent scholars to introduce the quaternions, octonions, sedenions, and trigintaduonions to research the electromagnetic fields, gravitational fields, weak nuclear fields, strong nuclear fields, quantum mechanics, gauge fields, and curved spaces and so forth. The algebra of trigintaduonions is able to discuss the physical quantities of four interactions, including the field potential, field strength, field source, linear momentum, angular momentum, torque, and force. In the field theories described with the algebra of trigintaduonions, the weak nuclear field is composed of three types of fundamental fields. These three fundamental fields, related to weak nuclear fields, can describe the physical properties of weak nuclear fields collectively. This is consistent with the conclusion of the electroweak theory. Meanwhile the strong nuclear field consists of three types of fundamental fields. These three fundamental fields relevant to strong nuclear fields may investigate the physical properties of strong nuclear fields mutually. It is coincident with the deduction of quark theory. According to the properties of trigintaduonions, one can deduce the Yang‐Mills equation related to the gauge fields. It means that the electromagnetic field occupies a quaternion space. The gravitational field owns one different quaternion space. The weak nuclear fields occupy three mutually independent quaternion spaces. The properties of weak nuclear fields are different from those of electromagnetic fields or gravitational fields. According to the multiplication table of trigintaduonion spaces, the strong nuclear fields own three conjugate quaternion spaces independent of each other. These explorations further deepen the understanding of the physical properties of weak and strong nuclear fields.

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Sedeonic Equations in Field Theory

Миронов

Mironov

2020

Adv. Appl. Clifford Algebras

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Sedeonic Field Equations for Dyons

Cited by 12 publications

References 32 publications

Octonion form of duality-invariant field equations for dyons

Octonion form of duality-invariant field equations for dyons

Gauge fields and four interactions in the trigintaduonion spaces

Sedeonic Equations in Field Theory

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